Six topologies of dynamic Bayesian Networks are evaluated for predicting the future user events: (1) Markov Chain of order 1, (2) Hidden Markov Model, (3) autoregressive Hidden Markov Model, (4) factorial Hidden Markov Model, (5) simple hierarchical Hidden Markov Model and (6) tree structured Hidden Markov Model. Goal of the investigation is to evaluate, which of these models has the best fit f...

We consider hidden Markov models as a versatile class of models for weakly dependent random phenomena. The topic of the present paper is likelihood-ratio testing for hidden Markov models, and we show that, under appropriate conditions, the standard asymptotic theory of likelihood-ratio tests is valid. Such tests are crucial in the specification of multivariate Gaussian hidden Markov models, whi...

— The aim of the present paper is to document the need for adapting the definition of hidden Markov models (HMM) to population studies, which rigorous interpretation typically requires the use of mixed-effects models, as well as for corresponding learning methodologies. In this article, mixed hidden Markov models (MHMM) are introduced through a brief state of the art on hidden Markov models and...

We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Markov models with multiple hidden state variables, multiscale representations, and mixed discrete and continuous variables. Although exact inference in these generalizations is usuall...

Inferences from time-series data can be greatly enhanced by taking into account multiple modalities. In some cases, such as audio of speech and the corresponding video of lip gestures, the different time-series are tightly coupled. We are interested in loosely-coupled time series where only the onset of events are coupled in time. We present an extension of the forward-backward algorithm that c...

A semi-Markov HMM (more properly called a hidden semi-Markov model, or HSMM) is like an HMM except each state can emit a sequence of observations. Let Y (Gt) be the subsequence emitted by “generalized state” Gt. The “generalized state” usually contains both the automaton state, Qt, and the length (duration) of the segment, Lt. We will define Y (Gt) to be the subsequence yt−l+1:t. After emitting...

We describe a method for learning statistical models of images using a second-order hidden Markov mesh model. We show that the Viterbi algorithm approach used for segmenting Markov chains can be extended to Markov meshes. The segmental k-means algorithm can then be applied to iteratively estimate the state transition matrix and the probability densities of the observations for the model. We als...

Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum circuits, and (3) we present a lea...

Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however, their classification performance is a drawback. In this paper we apply ideas from the field of density ratio estimation to bypass the difficult step of lear...

In this work, we present the first results for neuralizing an Unsupervised Hidden Markov Model. We evaluate our approach on tag induction. Our approach outperforms existing generative models and is competitive with the state-of-the-art though with a simpler model easily extended to include additional context.